Problem: Simplify. Remove all perfect squares from inside the square roots. Assume $y$ and $z$ are positive. $\sqrt{75yz^2}=$
Solution: $\begin{aligned} \sqrt{75yz^2}&=\sqrt{5^2\cdot z^2\cdot 3y} \\\\ &=\sqrt{5^2}\cdot\sqrt{z^2}\cdot\sqrt{3y} \\\\ &=5\cdot z\cdot\sqrt{3y} \\\\ &=5z\sqrt{3y} \end{aligned}$ In conclusion, $\sqrt{75yz^2}=5z\sqrt{3y}$